Fully utilizing the benefit of strong electrothermal feedback, we achieved the energy resolution of 6.6 eV (FWHM) at 5.9 keV and a fast response time of 74 μs with our bridge-type Ti/Au transition-edge sensor (TES) microcalorimeter. The energy resolution of this device was limited by a noise that was larger than the intrinsic noise and the readout noise. This noise only appeared when the current through the TES was large (≳10 μA) , and its level, defined as a fluctuation amplitude of the current through the TES, was in proportion to the inverse of the TES resistance. We also found that the TES sensitivity depended on the current through the TES, normalized with the critical current of the TES. When the current exceeded about 1% of the critical current, the TES sensitivity was significantly degraded. The critical current clearly correlated with the TES sensitivity, and hence the signal-to-noise ratio at the optimal operating point, among devices with different TES size and thickness. Thus, the critical current is one of the key parameters to determine the performance of the TES microcalorimeter.